Mixed-strategy minimax theorem without compactness

Steve Alpern, Shmuel Gal

Research output: Contribution to journalArticlepeer-review


The authors establish a new mixed-strategy minimax theorem for a two-person zero-sum game given in the normal form f:X×Y → R. This is interpreted in the usual way, so that if the minimizer picks a pure strategy x in X and the maximizer picks a pure strategy y in Y then the payoff (to the maximizer) is f(x, y). It is assumed that the pure strategy space X is a compact Hausdorff space, and that the mixed strategies available to the minimizer are the regular Borel probability measures on X, collectively denoted by B(X). The approach is asymmetric in that it is not assumed that the maximizer's pure strategies are necessarily topologized.

Original languageEnglish
Pages (from-to)1357-1361
Number of pages5
JournalSIAM Journal on Control and Optimization
Issue number6
StatePublished - 1988
Externally publishedYes

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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